let y, z be Element of X5; :: thesis: ( ( for x1, x2, x3, x4, x5, x6, x7 being set st x = [x1,x2,x3,x4,x5,x6,x7] holds
y = x5 ) & ( for x1, x2, x3, x4, x5, x6, x7 being set st x = [x1,x2,x3,x4,x5,x6,x7] holds
z = x5 ) implies y = z )
assume A19: for x1, x2, x3, x4, x5, x6, x7 being set st x = [x1,x2,x3,x4,x5,x6,x7] holds
y = x5 ; :: thesis: ( ex x1, x2, x3, x4, x5, x6, x7 being set st
( x = [x1,x2,x3,x4,x5,x6,x7] & not z = x5 ) or y = z )
assume A20: for x1, x2, x3, x4, x5, x6, x7 being set st x = [x1,x2,x3,x4,x5,x6,x7] holds
z = x5 ; :: thesis: y = z
consider xx1 being Element of X1, xx2 being Element of X2, xx3 being Element of X3, xx4 being Element of X4, xx5 being Element of X5, xx6 being Element of X6, xx7 being Element of X7 such that
A21: x = [xx1,xx2,xx3,xx4,xx5,xx6,xx7] by A1, Th94;
y = xx5 by A21, A19;
hence y = z by A21, A20; :: thesis: verum